156 



LOOMING, OR HORIZONTAL REFRACTION. 



Formula. half of the distance K c 5 but the total deviation of the light 



ivill not be twice the angular displacement of the point c, 

 unless K and « be equidistant from the surface. If however 

 the angular direction of the surface be known, as is almost 

 always the case in nature, the angle P K X, which is half 

 the deviation, may also be found by observation ; being, for 

 example, when the surface is horizontal, the actual angular 

 elevation of the image of the point?. The place of the ^ 

 surface L M, which limits the variable medium, may be 

 found from the measures of the actual elevation and the 

 displacement of the point g ; for its distance from /, the 

 middle point between g and its image, is always one fourth 

 of the elevation. The circumstances will be nearly similar 

 when K is either in the line L M, or a little above it, pro- 

 vided that s be below it ; but if both these points are above 

 it, there will be no double image. 



If however, the variation of the medium be continued, in 

 an inferior degree only, to the place of the eye and the ob- 

 ject, effects of a similar nature may still be sometimes pro- 

 duced : but it is not sufficient in this case to suppose with 

 Dr. Wollaston, that the curve indicating the density l\as a 

 contrary curvature; for it must be such, that the change of 

 density, and consequently the curvature" of the ray, must 

 vary more rapidly than the distance fiom the line joining the 

 eye and the object ; for example, if the curve be logarith- 

 mic, its subtangent must be considerably less than the great- 

 est distance of the bent ray from its chord ; otherwise there 

 can be no double image. Supposing the curvature of the 

 rays be as the distance from any given line, the form will 

 Object seen in be nearly that of the harmonic curve. But whenever the 

 its true place, ^-g^ can \y e seen m fa ^ rue p] ace? beside the appearance 



of one or more displaced images, it is obvious that both the 

 eye and the object must be situated in a uniform medium, 

 as we have hitherto supposed. 



Variation of 

 the medium 

 continued to 

 the eye and 

 the object 

 sometimes. 



II. 



